Discrete Differential Geometry
Discrete exterior calculus and structure-preserving operators on meshes.
Discrete Differential Geometry. Discrete exterior calculus and structure-preserving operators on meshes.
Foundations and canonical references
The standard treatments of discrete differential geometry approach the subject from complementary angles. Crane, Discrete Differential Geometry: An Applied Introduction (2018) is the anchor reference for the subject and lays out the core definitions, theorems, and worked examples that practitioners return to. Bobenko, Discrete Differential Geometry (2008) gives a parallel, more proof-oriented exposition of the same material and is widely used as a graduate text.
Open methodological questions for discrete differential geometry include sharpening the bridges between foundational theory and computational practice, extending classical results to broader or more structured settings, and integrating the techniques surveyed above with adjacent mathematical disciplines. The references listed in this page are the entry points that current work builds on.
Prerequisites
Sources
- textbook · primary · 2018Discrete Differential Geometry: An Applied Introductioncrane-2018
- textbook · primary · 2008Discrete Differential Geometrybobenko-2008, suris-2008
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